A mass on a spring on a spring oscillates back and forth and

A mass on a spring on a spring oscillates back and forth and completes one cycle in 2 seconds. Its maximum displacement is 5 cm. If the initial displacement is 5 cm., write an equation that models this motion.

Solution

Solution:

For the first one, the \'cycle of 2 seconds\' means that the function has a period of 2.

But recall that frequency equals 2 / period = 4.

In addition, a displacement of three translates into the idea that your function has an amplitude of three since

amplitude is nothing more than displacement away from the midline of the function.

Since the spring starts from a stretched position,

cos is appropriate since the initial displacement is non-negligible.

Therefore The equation is d= 5 cos 4(pi)t cm

If there are 528 vibrations per second, then there is one vibration, one \'cycle,\' every 1/528 second.

Since frequency equals 2 / period, w = 2 / (1/528) = 1056.